1. Introduction
The turbulent heat fluxes between the land surface and the atmosphere are a central component of Earth’s climate system. At the land surface, solar radiation is absorbed, transformed, stored, and released again into the atmosphere as sensible and latent heat. In this way, sensible and latent heat fluxes control the climate conditions within the boundary layer and constitute the lower boundary condition for all atmospheric circulations on Earth.
The partitioning of the turbulent heat fluxes in sensible and latent heat fluxes strongly depends on the amount of soil water available for evapotranspiration (McPherson 2007). If a sufficient amount is available, a major part of the incoming solar radiation is used for evapotranspiration instead of further warming the land surface. The latent heat fluxes are large and the sensible heat fluxes comparatively small. However, if the soil water supply for evapotranspiration is reduced and falls below a critical threshold, the latent heat fluxes are getting small and the sensible heat fluxes are becoming large. Thus, the available soil water amount for evapotranspiration is a key factor, shaping the near-surface climate conditions (Seneviratne et al. 2010).
To be able to simulate the near-surface climate conditions correctly, therefore, the available amount of soil water for evapotranspiration needs to be adequately estimated in climate models. But in general, it is a challenging task to quantify the soil water supply for evapotranspiration. It is a quantity that depends on two uncertain factors, the soil water content itself and the capability of plants to extract this water from the soil. On the one hand, the actual soil water content is generally unknown. First, because an exact simulation of the water input into the soil, i.e., of precipitation (e.g., Berg et al. 2013; Prein et al. 2013) and of irrigation (e.g., Sorooshian et al. 2012), is very difficult. Second, the general evapotranspiration characteristics of the vegetation cover are often poorly represented in climate models and in this way, the general release of water from the soil reservoir. In this context, important factors are the photosynthesis (e.g., Smallman and Williams 2019), stomatal conductance (e.g., Bonan et al. 2014), phenology and crop management (e.g., Sacks and Kucharik 2011), or the representation of the plant functional types in the model (e.g., Bonan et al. 2002; Sulis et al. 2015; Shrestha et al. 2018; Boas et al. 2021). Furthermore, large uncertainties exist concerning soil characteristics like the pore volume or the hydraulic conductivity (e.g., Mölders 2005; Gutmann and Small 2007), which control the water transport through and its distribution in the soil.
On the other hand, the capability of the plants to extract this water from the soil for transpiration is mainly determined by the plants access to the stored soil water, which in turn strongly depends on the root depths. But only limited observational data exist regarding the depth and density of root systems in the soils (e.g., Jackson et al. 1996; Schenk and Jackson 2002, 2003). The quantification of soil water extracted by plants is consequently also prone to errors. Thus, reliable information about the quantities which affect the actual soil water supply for evapotranspiration is limited. The parameter values used in global and regional climate models to simulate this water supply do consequently rarely correspond to the actual values. Therefore, the simulated amount of available soil water for evapotranspiration inevitably deviates from the actual amounts, necessarily affecting the simulation of the latent and sensible heat fluxes in climate models. As soon as the soil moisture content reaches a critical threshold, the evapotranspirative demand cannot be totally covered by soil water anymore and the surplus energy is transformed into soil warming and thus, sensible instead of latent heat fluxes (Seneviratne et al. 2010). If this critical threshold is reached in a climate model but not in nature, the evapotranspiration rates are systematically underestimated, if the threshold is reached in nature but not in the climate model, the opposite is the case.
The impact of a spuriously simulated threshold transgression is particularly large in evapotranspiration regimes which are temporally soil moisture–limited (Koster et al. 2006). This is the case in central and southern Europe during summer (Seneviratne et al. 2006; Berg et al. 2015). In such regimes, a high atmospheric demand for evapotranspiration is facing a small soil water supply. An inaccurately estimated critical threshold of the available soil water amount for evapotranspiration can consequently lead to a considerable over or underestimation of the evapotranspiration rates and thus, to biases in the near-surface temperatures. A well-known example for such an incorrect model behavior is the consistently simulated warm bias in summer in southern Europe in different model intercomparison studies (e.g., Hagemann et al. 2004; Jacob et al. 2007; Kotlarski et al. 2014; Mueller and Seneviratne 2014). In these studies, it is supposed that in most of the applied regional climate models (RCMs) and general circulation models (GCMs) summer precipitation and thus, the amount of available soil water for evapotranspiration is underestimated, resulting in a systematic overestimation of the near-surface temperatures.
In the literature several approaches were realized to reduce such systematic biases, which are associated with the available soil water amount for evapotranspiration, by improving individual subprocesses in climate models. For instance, an improved representation of the soil water supply for evapotranspiration was achieved by implementing a depth-dependent saturated soil hydraulic conductivity function in a land surface model (LSM) (Breil et al. 2018), or by considering lateral flow processes in the soil (Schlemmer et al. 2018). Moreover, a more realistic model adjustment to water limitations was achieved by taking into account the vertical redistribution of soil water by roots (Lee et al. 2005), and an implementation of dynamic roots into a LSM (Drewniak 2019).
In principle, such improvements of physical processes in LSMs constitute the conclusive and correct way to sustainably develop climate models. But an inaccurately estimated soil water supply for evapotranspiration can be caused by many different processes (e.g., inaccuracies related to the precipitation rates (e.g., Kotlarski et al. 2014), the atmospheric evapotranspiration forcing (e.g., Hagemann et al. 2004), the vertical (e.g., Breil et al. 2018) and horizontal (e.g., Schlemmer et al. 2018) soil water transport, or the soil water extraction by roots (e.g., Teuling et al. 2006; Shrestha et al. 2018). The physical reasons for moisture-related biases in the near-surface climate conditions can consequently differ, even within the same model domain. Additionally, the identification of these physical reasons is not a straightforward operation. Therefore, a lot of different model developments are needed to get rid of such biases without having the certainty that all model deficiencies can be redressed.
Thus, in order to improve the simulation of the near-surface climate conditions under soil moisture–limited conditions systematically, a method would be of great advantage which affects the simulation results only in specific regions and periods, where biases occur which are caused by a spuriously simulated soil water amount for evapotranspiration, irrespective of which physical process caused these modeled soil water deficiencies. Simulation results in other regions and periods should not be substantially affected. Therefore, the goal of the presented study is to develop a method which fulfills these requirements. For this purpose, a new modeling approach is introduced, by which the available amount of soil water for evapotranspiration is stochastically varied.
In general, stochastic modeling is an established method to overcome a systematic behavior of a deterministic model (Buizza et al. 1999; Palmer 2001). Thereby, in general, atmospheric model parameters are stochastically perturbed, to account for the uncertainties in sub-gridscale processes and to increase the degrees of freedom in the climate model. In this way, different model states can be reached, which are consistent with the parameter uncertainty and thus, the natural variability of the simulated processes. As a consequence, systematic model biases can potentially be mitigated (Berner et al. 2011).
This stochastic method will be applied on the soil water supply for evapotranspiration to correct the associated systematic model biases. In this context, the focus will be on the uncertainties related to the root depth. The root depth defines the depth of the soil column from which water can be extracted and consequently controls the amount of available soil water for evapotranspiration. In the presented study, this amount will be perturbed by a stochastic variation of the root depth in simulations with the RCM COSMO-CLM (CCLM; Rockel et al. 2008), coupled to the land surface model VEG3D (Breil et al. 2019). Since the depth of roots is, apart from the vegetation type, also related to the general climate and soil conditions, root depths can considerably vary within the same vegetation type (Schenk and Jackson 2002). The sub-gridscale uncertainty is consequently high. The root depth variation will therefore be performed within a characteristic and realistic range (Schenk and Jackson 2003). In this way, plausible root depths can be applied in regional climate simulations, which are better representing the large heterogeneity of root depths in real soils and thus potentially improve the simulation of the latent heat fluxes and the near-surface temperatures.
The study is structured as follows. In section 2, the stochastic parameterization of the root depths is described in detail. The impact of this stochastic variation on the regional climate simulations results in Europe is investigated and discussed in section 3. Conclusions are drawn in section 4.
2. Method
a. Stochastic variation of the soil water supply for evapotranspiration
The goal of this study is to develop a method by which systematic model biases in temporally soil moisture–limited evapotranspiration regimes can be reduced, without negatively affecting evapotranspiration processes in other regions and periods. For this purpose, the available soil water amount for evapotranspiration will be stochastically varied. Since this available soil water amount is determined by the soil water content within the rooted soil profile, a stochastic variation can be performed in three different ways: 1) the variation of the soil water content within the rooted soil profile, 2) the variation of the water input into the soil (precipitation), or 3) the variation of the root depth. In physical terms, a stochastic perturbation of the soil water content (variation 1) seems to be the obvious choice, since variations of the soil water content are constantly occurring in nature. But such perturbations would artificially add and remove water from the simulated water cycle and the conservation of mass would be violated. Additionally, sudden changes in the soil water content can cause numerical inconsistencies in the model, potentially resulting in a breakdown of model simulations. A stochastic perturbation of the soil water content is therefore not an appropriate method. Another opportunity would be a stochastic variation of the precipitation partitioning into infiltration and runoff (variation 2). In this way, the soil water content would be changed without violating the conservation of mass. But changes in the soil water input would artificially change the actual soil water content and inevitably disturb the soil moisture memory. An associated soil moisture deficiency/surplus would consequently affect the land–atmosphere interactions over long periods (Orth and Seneviratne 2012).
Such difficulties can be avoided by a stochastic variation of the root depths (variation 3). By applying this method, the capability of plants to extract water from the soil is changed. In this way, the available amount of soil water for evapotranspiration is varied without changing the soil water content itself. Due to this, the conservation of mass and the soil moisture memory are preserved and the consistency of the simulated physical processes in the model is guaranteed. Potential numerical problems related to abrupt soil moisture changes are consequently avoided.
b. Root depth variation
In state of the art LSMs, the root depth is derived from the vertical root density distribution. This profile describes the root density in different soil depths down to the maximum root depth (Schenk and Jackson 2003), and therefore quantifies the ability of plants to transpire water from the respective soil layers. Since the root density distribution depends on the plant type, vegetation specific root profiles are applied in LSMs. But the distribution of these root profiles (and thus the root depth) is associated with large uncertainties. On the one hand, the maximum root depth depends on the mechanical and hydraulic characteristics of the soils. On the other hand, root profiles are strongly affected by the prevailing climate conditions and the general water availability (Schenk and Jackson 2002). As a consequence, large sub-gridscale differences can exist, which are not considered in the coarse model resolution. In a methodological sense, therefore, a stochastic variation of the root depth can be considered reasonable.
This stochastic root depth variation is performed as follows: the root density profile in each model grid box is shifted by using a random number generator to create uniformly distributed numbers between −1.0 and 1.0. For positive random numbers, the whole root density profile with its maximum depth is shifted downward in the soil column, for negative random numbers the root profile is shifted upward. In this way, the vegetation specific shape of the density distribution is preserved, but the depth from which water can be extracted is changed. Since the stochastic root profile variation is uniformly distributed over the whole model domain and performed for each model grid box separately, the root depths are increased for 50% of the grid boxes in the model domain and reduced for the other 50%. This is approximately also the case for the available amount of soil water for evapotranspiration. The total potential of the soil to provide water for evapotranspiration is therefore essentially preserved over Europe. This is also the case for spatial soil moisture patterns, since the soil water contents are not directly changed, only the capability of the plants to extract the soil water for evapotranspiration.
In an LSM, the soil column in a model grid box is divided in different layers. By means of this layering, the model is able to solve the vertical heat and water transport through the soil, by using finite differences. This vertical grid structure has to be considered when the root depths are stochastically varied. An example for how the vegetation specific root density distribution is adapted to the vertical grid structure of the LSM is shown in Table 1 and Fig. S1 in the online supplemental material for cropland (the dominant land use class in Europe). In the case of positive random numbers, this means that the root density distribution in each layer is proportionally shifted downward into the next soil layer. The new root density in a soil layer is therefore a linear combination of the actual root density and the one of the overlying soil layer. For the maximum perturbation of 1.0, the complete root profile (and thus the root depth) is displaced by one soil layer. For negative random numbers, an upward layer displacement is performed. This root profile variation is within the scope of the observed root depth range of the respective vegetation types (Schenk and Jackson 2002) and constitutes therefore a realistic and plausible parameter range to account for the sub-gridscale root depth uncertainties.
Layer depth and root density distribution according to (Schenk and Jackson 2003) used in CCLM-VEG3D, for the reference run (ref) and the maximum stochastic variations (stoch-1.0 and stoch1.0), exemplary shown for cropland, the dominating land use class in Europe.
The root depth values are varied yearly, always at midnight on the first day of a year. At this time, evapotranspiration rates are low and sudden jumps in the latent heat flux calculation are avoided, which could cause numerical model inconsistencies. This yearly stochastic root depth variation is a quite long interval in comparison to stochastic modeling approaches for the atmosphere (e.g., Buizza et al. 1999). But since the transport and exchange processes proceed much slower in the soil than in the atmosphere, the chosen time interval between the respective stochastic parameter perturbations is necessary to achieve an effect of the variations on the soil conditions. Furthermore, by means of yearly stochastic variations, a physically consistent development of the soil conditions is guaranteed for a whole vegetation period. In this way, a seasonal soil moisture memory is preserved, which is essential to consistently simulate the development of the soil conditions during a year (Dirmeyer and Halder 2017).
c. Expected effects
In principle, two different types of evapotranspiration regimes are distinguished: energy-limited regimes and soil moisture–limited regimes (Seneviratne et al. 2010). In wet regimes, evapotranspiration is only limited by the available energy, in dry regimes, on the contrary, evapotranspiration is only limited by the moisture availability. In transitional regimes like the European midlatitudes, evapotranspiration can be temporally constraint by both, either energy or moisture. While evapotranspiration is generally energy limited during winter and during summer in northern Europe, soil moisture limitation can arise during European summer in central and southern Europe (Seneviratne et al. 2006; Berg et al. 2015). Although a poorly represented capability of plants to extract water from the soil can cause certain model biases also in energy-limited regimes, systematic model biases, which are associated to an uncertain soil water supply for evapotranspiration, mainly occur under soil moisture–limited conditions. Therefore, a method which improves the simulated climate conditions in summertime soil moisture–limited regimes, without inducing negative effects in other regions and periods would be beneficial. For this purpose, the method needs to account for different attributes under energy-limited and soil moisture–limited conditions, respectively.
The expected effects of a stochastic root depths variation on energy-limited and soil moisture–limited evapotranspiration regimes are conceptually described in Fig. 1. In energy-limited regimes, significant impacts of a stochastic root depth variation are not expected (Fig. 1a). Since the radiative energy input is generally small in such regions, the low evaporative demand should be still covered after slight variations of the available soil water amount for evapotranspiration. But in soil moisture–limited regimes significant effects of such a stochastic variation can be expected (Fig. 1b). These effects are conceptually shown in Fig. 2. Since in soil moisture–limited regimes upper soil layers are generally drier than the deep soil layers (due to the higher root density in the upper layers (Table 1) and an associated enhanced water extraction by transpiration), a root depth variation must inevitably affect the available amount of soil water for evapotranspiration. A uniformly distributed stochastic root depth variation will increase the water supply for evapotranspiration in 50% of the grid boxes in the model domain and will reduce it in the other 50%. In the case that the available soil water amount for evapotranspiration is realistically estimated in a climate model, the yearly varying negative and positive moisture perturbations should counteract each other and the near-surface conditions should spatially and temporally not be affected on the climatological mean. But if the soil moisture availability is not correctly estimated in a climate model, such a balance of the positive and negative moisture perturbations cannot be expected. In the case of an overestimated soil water supply for evapotranspiration, a further increase of the soil water availability in 50% of the model grid boxes by increased root depths should not additionally enhance the already overestimated evapotranspiration rates. But for the other 50% of the model grid boxes, the root depth reduction should have certain implications. In these grid boxes, the soil water availability for evapotranspiration should be reduced, resulting in a reduction of the overestimated evapotranspiration rates. Since such a root depth reduction is not constant over the simulation and can occur every year in another model grid box, near-surface climate conditions should in mean be improved in all grid boxes located in soil moisture–limited regimes. In the case of an underestimated soil water supply for evapotranspiration, as it is simulated in summer in Europe in many climate models, a further reduction of the root depths in 50% of the model grid boxes should not additionally reduce the already existing water limitations for evapotranspiration. But an increase in the other 50% of the model grid boxes should increase the soil water availability and thus the evapotranspiration rates. This should lead in mean to a reduced bias in the near-surface climate conditions in soil moisture–limited regimes. Due to this asymmetric effect on the soil water supply for evapotranspiration, the stochastic root depth variation potentially constitutes a method to systematically reduce biases in summertime soil moisture–limited evaporation regimes, without causing negative side effects in energy-limited regimes. In this context, the physical reason for the spuriously simulated soil water supply for evapotranspiration (over or underestimation of precipitation, root depth, etc.) is irrelevant, since the method does not improve the simulated soil water supply itself. Only the negative effects of these model deficiencies on the near-surface climate conditions are compensated. In this way, the initially stated requirements for an adequate method should therefore be fulfilled.
Expected effects of a stochastic root depth variation in different grid boxes: (left) increased root depth and (right) reduced root depth on (a) energy-limited and (b) soil moisture–limited evapotranspiration regimes. The black line indicates the root depth in the reference run. Latent heat fluxes (L) are drawn in red and sensible heat fluxes (S) in blue. The T represents the near-surface temperatures.
Citation: Journal of Hydrometeorology 22, 7; 10.1175/JHM-D-20-0265.1
Expected effects of (right) a stochastic root depth variation in soil moisture–limited evapotranspiration regimes in comparison to (left) a standard model with unperturbed roots. Shown are the effects on the available amount of soil moisture for evapotranspiration (Wavail), evapotranspiration (ET), and near-surface temperature (T) for three different types of standard model behavior: (top) Wavail is overestimated (red) and T is underestimated (blue), (middle) Wavail and T are correctly simulated (black), and (bottom) Wavail is underestimated (blue) and T is overestimated (red). The colored arrows indicate the induced tendency changes for Wavail, ET, and T (increased in red; reduced in blue).
Citation: Journal of Hydrometeorology 22, 7; 10.1175/JHM-D-20-0265.1
d. Simulation setup
Regional climate simulations with COSMO-CLM (CCLM; Rockel et al. 2008) coupled to the LSM VEG3D (CCLM-VEG3D; Breil et al. 2019) are performed for Europe. COSMO-CLM is the climate version of the former three-dimensional nonhydrostatic weather forecast model COSMO (Baldauf et al. 2011) of the German Weather Service (DWD). The applied physical parameterizations, dynamics, and numerics in CCLM are described in detail in Doms and Baldauf (2018). VEG3D is a multilayer LSM that has been evaluated in several studies (Breil and Schädler 2017; Breil et al. 2018). Its parameterizations are described in Breil and Schädler (2017) and Breil et al. (2021).
In a first step, a reference simulation is performed with the default root depths used in the CCLM-VEG3D model system based on Schenk and Jackson (2003). In a second step, three stochastic simulations with perturbed root depths are performed. In this way, a stochastic ensemble is created to consider the whole range of possible effects of the stochastic parameter variation. Since no differences exist in the setup of the ensemble simulations and the reference run beside the stochastically perturbed root depths, differences must be caused by the stochastic root depth variation. To evaluate the impact of the applied root depths on the near-surface climate conditions, all results are compared to the E-OBS observational dataset, a European daily high-resolution gridded dataset of surface temperature and precipitation (Haylock et al. 2008).
All simulations are driven by ERA-Interim reanalyses (Dee et al. 2011) at the lateral boundaries and at the lower boundary over sea. The simulation period is 1979–2015. The simulation results are evaluated for the period 1986–2015, so that a spinup of 7 years is performed for each simulation. The model domain is identical to the Coordinated Downscaling Experiment-European Domain (EURO-CORDEX; Jacob et al. 2014), comprising the whole European continent, the Mediterranean Sea, North Africa, and the eastern part of the North Atlantic. The spatial horizontal resolution is 0.44°, resulting in 106 × 103 horizontal grid points. In the atmosphere 40 vertical levels are used. The time step is 300 s.
The distribution of the different land use classes and soil types within the model domain is illustrated in Fig. 3. The land use classes and soil types are derived from the GLC2000 dataset (Bartholomé and Belward 2005). In central and southern Europe, cropland is the dominating land use, and in Scandinavia evergreen forest is dominating. Loam and sandy loam are the prevailing soil types all over Europe.
Distribution of the different (a) land use classes and (b) soil types in CCLM-VEG3D.
Citation: Journal of Hydrometeorology 22, 7; 10.1175/JHM-D-20-0265.1
3. Results and discussion
a. Characteristics of the reference run
The differences in seasonal mean 2m temperatures and precipitation sums between the CCLM-VEG3D reference run and the E-OBS observational dataset are shown in Fig. 4 for the winter (DJF) and the summer season (JJA) over the period 1986–2015. The red colors indicate regions with a positive bias, the blue colors show areas with a negative bias. In both seasons, the CCLM-VEG3D results are characterized by an extensive warm bias over large parts of Europe. In winter, a warm bias is simulated all over Europe, except the Mediterranean region. In summer, a warm bias occurs in central, eastern, and southern Europe, as well as northern Africa, while a cold bias is simulated over Scandinavia and the Iberian Peninsula. The precipitation amounts in CCLM-VEG3D are all over Europe overestimated in winter, while the precipitation amounts are underestimated in summer, especially in eastern and southeastern Europe.
Differences in the simulated seasonal mean (a),(b) 2-m temperatures (K) and (c),(d) precipitation sums (mm) between the CCLM-VEG3D reference run and the E-OBS observational dataset for (left) the winter (DJF) and (right) the summer season (JJA) for the evaluation period 1986–2015. The black boxes in (b) indicate the relevant subregions central Europe (CE), eastern Europe (EA), southeastern Europe (SEA), Scandinavia (SC), northern Africa (NA), and Iberian Peninsula (IP), which are discussed in the study.
Citation: Journal of Hydrometeorology 22, 7; 10.1175/JHM-D-20-0265.1
Since in winter, evapotranspiration is generally energy limited, a stochastic root depth variation should not affect the CCLM-VEG3D simulation results during this season. Therefore, a reduction of the general winter biases in the reference run cannot be expected. This is also the case for the cold bias in the energy-limited evapotranspiration regime of Scandinavia in summer (e.g., Teuling et al. 2009). A different situation constitutes the simulated cold bias at the Iberian Peninsula in summer. In this region, evapotranspiration is soil moisture limited during summer (e.g., Berg et al. 2015). In principle, such a cold bias can possibly be related to an overestimation of the evapotranspiration rates in the climate model (see section 2c). But this is not the case in the CCLM-VEG3D reference simulation. Figure 5 shows that in CCLM-VEG3D the simulated latent heat fluxes in summer are already very low at the Iberian Peninsula. In the central and southern parts of the Iberian Peninsula almost no evapotranspiration takes place. In this area, precipitation sums are very low during summer (e.g., Vicente-Serrano et al. 2014), resulting in dry soils and low evapotranspiration rates. Thus, the simulated cold bias cannot be caused by an overestimated evapotranspiration and the associated cooling effect in the model. But beside for soil moisture reasons, temperature biases can also be triggered by many other model deficiencies related to the radiation balance and the vertical heat transport. Zhou et al. (2017), for instance, showed that a cold bias, which occurs in several reanalyses datasets in China, is caused by overestimated surface albedo values. In the case of the Iberian Peninsula, the results of Johannsen et al. (2019) indicate that the cold bias is related to a misrepresentation of the vegetation cover in the GLC2000 dataset (Bartholomé and Belward 2005), from which the vegetation characteristics in this study are also derived. In this dataset, vegetation cover in the Iberian Peninsula is overestimated, resulting in an overestimated surface roughness and associated underestimation of the surface temperatures. Thus, since the cold bias at the Iberian Peninsula is not related to deficiencies in the simulated soil water supply, a reduction of the cold bias is not possible by a stochastic root depth variation.
Simulated seasonal mean latent heat fluxes (W m−2) in summer for the CCLM-VEG3D reference run for the evaluation period 1986–2015.
Citation: Journal of Hydrometeorology 22, 7; 10.1175/JHM-D-20-0265.1
In central, eastern, and southern Europe, the results of the CCLM-VEG3D reference run are comparable to the results of other RCMs and GCMs, documented in several model intercomparison studies (e.g., Kotlarski et al. 2014; Mueller and Seneviratne 2014). Especially the summertime warm bias in southern and southeastern Europe is typical for climate simulations in Europe (e.g., Hagemann et al. 2004; Jacob et al. 2007; Kotlarski et al. 2014; Mueller and Seneviratne 2014). The warm bias in these regions is most likely associated to the underestimated precipitation sums in summer (Fig. 4d) and thus, an underestimated soil moisture supply. Since in CCLM-VEG3D, summer evapotranspiration is soil moisture limited in central, eastern, and southern Europe and the vegetated parts of northern Africa, a stochastic root depth variation should affect the simulation results in these regions and potentially reduce the systematic warm bias.
b. Effects of stochastic modeling on the seasonal climate conditions
The impact of stochastically varied root depths on the CCLM-VEG3D simulation results is shown in Fig. 6 for the mean seasonal latent and sensible heat fluxes in winter and summer. Shown are the differences between the stochastic ensemble mean and the reference simulation over the period 1986–2015. Here and in the following we will only show the results of the stochastic ensemble mean, since the simulation results are in all three ensemble members nearly identical (see Fig. S2 in the supplemental material). Thus, the simulated effects of the stochastic root depth variation are very robust. By showing the ensemble mean, therefore, the general effects of the stochastic approach can be described consistently.
Differences in the simulated seasonal mean (a),(b) latent and (c),(d) sensible heat fluxes (W m−2) for the (left) winter and (right) summer season between the CCLM-VEG3D stochastic ensemble mean and the reference run for the evaluation period 1986–2015.
Citation: Journal of Hydrometeorology 22, 7; 10.1175/JHM-D-20-0265.1
As expected, in winter almost no differences occur between the stochastically perturbed simulations and the reference run for both, the latent and the sensible heat fluxes. This is also the case for the latent heat fluxes in the energy-limited evapotranspiration regimes of northern Europe and of the mountain areas in central and eastern Europe (Alps and Carpathian Mountains) during summer. Moreover, further grid boxes with no increase in the latent heat fluxes are visible in central Europe. These grid boxes are covered by forests (Fig. 3) and are located in the transition zone between the very dry areas of southern Europe and the humid areas of northern Europe. In this transition zone, evapotranspiration is generally soil moisture limited in the reference run during summer, but not as pronounced as in southern Europe. Thus, a relatively increased amount of soil water for evapotranspiration, as available in forested areas due to the deep reaching root system, can prevent the soil to become moisture limited. Therefore, a stochastic root depth variation does not result in increased latent heat fluxes in these forested grid boxes in the transition zone. But in the soil moisture–limited regimes of central, eastern, and southern Europe and northern Africa (Seneviratne et al. 2006; Berg et al. 2015) the evapotranspiration rates are systematically increased by the stochastic root depth perturbation. Accordingly, the sensible heat fluxes are systematically reduced in the stochastic simulations during summer.
The increased evapotranspiration rates in summer affect also the mean seasonal atmospheric conditions in the stochastic ensemble. Over large parts of the model domain the mean cloud cover is increased (Fig. 7), due to the increased moisture release into the atmosphere. As a result, the mean seasonal net shortwave radiation in summer is reduced in the stochastic simulations. But again, no substantial differences occur in winter in comparison to the reference run.
Differences in the simulated seasonal mean (a),(b) cloud cover (%) and (c),(d) net shortwave radiation (W m−2) for the (left) winter and (right) summer season between the CCLM-VEG3D stochastic ensemble mean and the reference run for the evaluation period 1986–2015.
Citation: Journal of Hydrometeorology 22, 7; 10.1175/JHM-D-20-0265.1
According to the reduced net shortwave radiation (Fig. 7) and the increased evapotranspiration and the associated cooling effect (Fig. 5) in the stochastic simulations, colder mean near-surface temperatures are simulated in summer (Fig. 8). This near-surface temperature reduction is particularly pronounced in eastern and southern Europe. A temperature reduction is also simulated for the vegetated surfaces in northern Africa (Fig. 3). In northern Europe, a slight temperature reduction is simulated in the eastern parts of Scandinavia and no temperature reduction is simulated in the western parts. Differences between the stochastic ensemble and the reference run do not occur during winter. This is also the case for mean seasonal precipitation sums in winter. In summer, on the contrary, the mean precipitation sums are increased almost all over Europe, as a consequence of the increased evapotranspiration rates in the stochastic root depth simulations (Fig. 7). An exception is the western and southern parts of the Iberian Peninsula. Here no differences in the precipitation sums are simulated. But since there is almost no rain during summer (e.g., Vicente-Serrano et al. 2014), this could be expected.
Differences in the simulated seasonal mean (a),(b) 2-m temperature (K) and (c),(d) precipitation sums (W m−2) for the (left) winter and (right) summer season between the CCLM-VEG3D stochastic ensemble mean and the reference run for the evaluation period 1986–2015.
Citation: Journal of Hydrometeorology 22, 7; 10.1175/JHM-D-20-0265.1
The effects of these induced changes in the mean seasonal climate conditions, by a stochastic root depth variation, on the general model biases are shown in Fig. 9. The impacts on the winter biases are not shown, since no substantial effects on the mean seasonal winter conditions could be observed (Figs. 5–7). The reduced near-surface temperatures in the stochastic ensemble lead to a considerable reduction of the systematic warm bias in central, eastern, and southern Europe. In northern Africa, simulation results are additionally improved for vegetated surfaces (Fig. 3). These systematic reductions of the soil moisture induced warm biases in the stochastic ensemble compared to the reference run are statistically significant at the 95% level. By performing a Wilcoxon rank sum test, it was tested whether the squared errors of the mean monthly 2-m temperatures are in all three stochastic ensemble members lower than the squared errors of the reference run.
Differences in the simulated seasonal mean (a),(b) 2-m temperatures (K) and (c),(d) precipitation sums (mm) between (left) the CCLM-VEG3D reference run and the E-OBS observational dataset and (right) the CCLM-VEG3D stochastic ensemble mean and the E-OBS observational dataset in summer for the evaluation period 1986–2015. The gray lines indicate grid boxes in which the reductions of the squared errors of the mean monthly 2-m temperatures in (b) and precipitation sums in (d), over the whole simulation period of all three stochastic ensemble member, are significant at a 95% level in a Wilcoxon rank sum test in comparison to the reference run.
Citation: Journal of Hydrometeorology 22, 7; 10.1175/JHM-D-20-0265.1
In northern Europe, the cold bias is not substantially changed by the stochastic root depth variation as it was expected for energy-limited evapotranspiration regimes (section 2c). But at the Iberian Peninsula, the cold bias in the reference run is further increased. As already showed in section 3a, this bias cannot be soil moisture induced. This is confirmed by the increased evapotranspiration rates in the stochastic simulations (Fig. 6). Such an evapotranspiration increase should only occur in regions with underestimated evapotranspiration rates as they are indicated by the low rates in the reference run (Fig. 5). But this evapotranspiration deficiency should result in a warm bias, which is not observed. This warm bias must therefore be superimposed by another model deficiency, which is most likely an overestimation of the vegetation cover (Johannsen et al. 2019), resulting in an overall cold bias at the Iberian Peninsula in the reference run. In the stochastic root depth simulations, this cold bias is then further intensified by counteracting the underestimation of the evapotranspiration rates (Fig. 9). But the intensification of the cold bias at the Iberian Peninsula is not statistically significant.
With respect to precipitation, the stochastic root depth variation considerably reduces the dry bias in central, eastern, and southeastern Europe, due to the increased evapotranspiration rates in summer and the associated increased precipitation sums. For eastern and southeastern Europe, these improved precipitation sums are statistically significant (Fig. 9).
c. Effects of stochastic modeling on climate extremes
The results of recent studies show that the amount of available soil water for evapotranspiration strongly affects the characteristics of climate extremes, such as heat waves and droughts (Fischer et al. 2007; Vautard et al. 2007; Hirschi et al. 2011; Miralles et al. 2014; Whan et al. 2015). Thus, a stochastic variation of the root depth can also have considerable impacts on the development and the intensity of these climate extremes. In the following, therefore, the potential effects of the stochastic parameterization on both climate extremes will be further investigated.
Figure 10 shows the bias of the 95th percentile of the simulated daily maximum temperatures for the reference run (Fig. 10a) and the stochastic ensemble mean (Fig. 10b) in comparison to the observed values in the E-OBS dataset within the evaluation period (1986–2015). The bias of the reference run exhibits the same spatial patterns as already seen for the seasonal mean near-surface temperatures in summer (Fig. 9a). In central, eastern, and southern Europe as well as northern Africa, the extreme summer temperatures are overestimated in the reference simulation. In northern Europe, the extreme summer temperatures are underestimated. But in contrast to the mean seasonal near-surface temperatures, the cold bias at the Iberian Peninsula is less pronounced. Thus, a stochastic root depth variation and an associated increase in the evapotranspiration rates (Fig. 6b) lead to a further underestimation of extreme summer temperatures at the Iberian Peninsula (Fig. 10b). This circumstance confirms that the general cold bias of the seasonal mean near-surface temperatures in summer at the Iberian Peninsula (Fig. 9a) is not associated with overestimated evapotranspiration rates in the reference run as already stated in section 3a. If a cold bias in the seasonal mean near-surface temperatures would be caused by such an overestimated evaporative cooling, the cold bias should be strongest for the daily maximum temperatures, as evapotranspiration depends on the diurnal temperature cycle. Since this is not the case as shown for the bias of the 95th percentile of the daily maximum temperatures (Fig. 10a), the cold bias must be caused by other processes, like an overestimation of the vegetation cover as stated by Johannsen et al. (2019).
Bias of the 95th percentile of the simulated daily maximum temperatures (K) for (a) the CCLM-VEG3D reference run and (b) the CCLM-VEG3D stochastic ensemble mean in comparison to the observed values in the E-OBS dataset within the evaluation period (1986–2015). Differences in the number of simulated and observed drought days within the evaluation period (1986–2015) for the CCLM-VEG3D reference run and the CCLM-VEG3D stochastic ensemble mean in comparison to E-OBS.
Citation: Journal of Hydrometeorology 22, 7; 10.1175/JHM-D-20-0265.1
In central, eastern, and southern Europe as well as northern Africa, the overestimation of extreme summer temperatures (Fig. 10a) is considerably reduced by the stochastic root depth variation (Fig. 10b). This bias reduction is again similar to the one of the seasonal mean near-surface temperatures (Fig. 9b). As a result, the representation of extreme summer temperatures is improved for large parts of Europe by performing a stochastic root depth variation.
The impact of the stochastic root depth variation on droughts is assessed by comparing simulated and observed effective drought index (EDI) values (Byun and Wilhite 1999). The EDI is a measure for the water input and availability in a climate system. For each day of the evaluation period, the daily precipitation sums of the preceding 365 days are accumulated and weighted by a reduction function (increasing weights from day 365 to day 1). This accumulated precipitation sum is then calculated as anomaly to its mean climatological sum and normalized by the standard deviation. Thus, positive values represent humid conditions, negative values dry conditions. According to Khodayar et al. (2015), days with EDI values smaller than −2 are regarded as climatological extreme droughts. The number of simulated and observed drought days within the evaluation period (1986–2015) are counted and compared with each other (Figs. 10c,d). The differences between the reference run and the observations are shown in Fig. 10c, the differences between the stochastic ensemble mean and E-OBS are shown in Fig. 10d. The bias of the reference run for the number of drought days does not show any systematic spatial patterns (Fig. 10c). All over Europe, areas with an overestimated number of drought days alternate with areas with an underestimated number of drought days. The same noisy picture is found for the bias of the stochastic ensemble mean (Fig. 10d). The areas of overestimated as well as underestimated drought days are similar in location and amount to the reference run. Just slight improvements occur over western and central Europe. Thus, the representation of drought days is not substantially improved by the stochastic root depth variation. The increase in mean seasonal summer precipitation in the stochastic simulations (Fig. 8d) does consequently not essentially affect (reduce) the number of drought days. Only at first glance this is surprising, because droughts are strongly associated with precipitation deficits in winter (e.g., Vautard et al. 2007). The soil water reservoir is in such cases not entirely refilled, resulting in low latent heat fluxes and high sensible heat fluxes already in early summer. A production of warm air masses is the consequence, favoring the development of heat waves in summer. Since the stochastic root depth variation does not change the precipitation amounts in the winter season (Fig. 8c), the representation of drought days is also not affected in comparison to the reference run.
4. Conclusions
In this study, a new method is introduced to reduce systematic temperature biases in soil moisture–limited evapotranspiration regimes, which are frequently simulated in global and regional climate simulations (e.g., Hagemann et al. 2004; Jacob et al. 2007; Kotlarski et al. 2014). In the climate models, spuriously simulated amounts of available soil water for evapotranspiration lead to over or underestimated evapotranspiration rates (e.g., Mueller and Seneviratne 2014). As a result, the sensible heat transport into the atmosphere is inaccurately simulated and biases in the near-surface temperature are the consequence. To get rid of these systematic biases, therefore, many efforts were made to improve the model representation of the physical processes causing the spuriously simulated soil water supply for evapotranspiration (e.g., Schlemmer et al. 2018; Drewniak 2019), such as wrong precipitation amounts (e.g., Kotlarski et al. 2014) or root depths (e.g., Teuling et al. 2006). However, an improvement of all these different model components is a very challenging or even almost impossible task, since all these processes depend on a variety of other processes and therefore, are associated with large uncertainties. Thus, a simple method would be of great advantage, which could compensate the negative effects of soil moisture induced biases in soil moisture–limited regimes, irrespective of which physical process caused these modeled soil water deficiencies, without affecting the results in other regions or periods.
To achieve this goal, a stochastic root depth variation was applied on regional climate simulations for Europe. The suitability of stochastic modeling approaches to account for model uncertainties, was already successfully demonstrated in several studies for atmospheric processes (e.g., Buizza et al. 1999) and land–atmosphere interactions (Breil and Schädler 2017). With this method the available amount of soil water for evapotranspiration in each grid box is randomly varied, but within a meaningful range. This stochastic parameterization has certain systematic implications on the partitioning of the turbulent heat fluxes in soil moisture–limited evapotranspiration regimes. Systematically overestimated evapotranspiration rates are reduced, systematically underestimated rates are increased, with the consequence that near-surface temperature biases are systematically improved. Correctly estimated near-surface climate conditions as well as simulation results in energy-limited evapotranspiration regimes are not substantially affected by the method.
Nevertheless, the method has certain limitations. For one thing, the stochastic root depth variation is not able to improve the simulation of summer droughts (Fig. 10). This shortcoming of the method is mainly caused by the fact that the stochastic parameterization does not affect/improve precipitation amounts in winter, which are essential for the refilling of the soil water reservoir and thus, the development of droughts. Furthermore, in climate models, model deficiencies do often compensate each other. The reduction of the negative effects of a spuriously simulated soil water supply for evapotranspiration by a stochastic root depth parameterization can consequently disturb the “balance” of these model deficiencies and temperature biases can emerge in regions where they were not found before. Thus, the stochastic variation of the root depths can in some cases lead to a deterioration of the model performance. On the other hand, these possible negative effects of the method can be used to reveal previously hidden model deficiencies and, in this way, can provide important information for further model developments.
Therefore, stochastic root depth modeling and its asymmetric effect on evapotranspiration constitutes a simple method to reduce systematic soil moisture induced temperature biases in temporally soil moisture–limited evapotranspiration regimes, irrespective of which physical process caused the modeled soil moisture deficiencies. The simulation of the soil water supply for evapotranspiration itself is in this context not improved, only the negative effects of these model deficiencies on near-surface climate conditions are compensated. Thus, the method should be applicable in any regional or global climate model. To validate this hypothesis, in follow-up studies the method will be implemented in different global or regional climate model systems and applied on different soil moisture–limited regimes all over the world.
Acknowledgments
Marcus Breil acknowledges funding by the Federal Ministry of Education and Research in Germany (BMBF) under the ClimXtreme research program (FKZ: 01LP1902N). All simulations were performed at the German Climate Computing Center (DKRZ).
Data availability statement
The data used in this study are available upon request from the corresponding author.
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